Export 1920x1080 prores 4444 quicktime movie at 'current settings': Upon inspecting the output, the frame is displaying at 1888x1062. Why?

Someone explained to me that this is a quirk of QT 10; he pointed out that QT7 displays it correctly at 1920x1080. But even in QT7 (below left), the inspector displays the following:

Where does FCP (or QT) get this 1888x1062 dimension and why doesn't QT10 display it correctly? More importantly, is there anything wonky about the quicktimes that could come back and haunt me elsewhere in our (vfx) pipeline?

But as said, what counts is not the displayed size, but the real size. This from your screen shots is totally correct.
You may try to hit cmd-1 in the QT7 Player and refresh the Inspector. You also may use cmd-J in QT 7 Player to figure out the discrepancy about real and display size.
There are some apps which really do use the display size, but as long you do not save the files displayed in QT Player there won't be any issue.

Some edit to my earlier post is are a bit of math.
If your display doesn't match, means has enough space for title bars in the vertical, then this scenario can happen:
The title bar uses 16 px, subtract this from the actual image height. You'll get 1064 px displayed image height. This divided by 9 results in 118.222222222222222 which is not possible to display with an 16:9 picture
since picture width would be 1891.555555555555556.
So it's rounded down to 118. Resulting display will be 118x9 = 1062 and 118x16 = 1888

In QuickTime Pro 7 you have access to the aperture settings, where you can force it to display full size. QuickTime X does not have these controls. Hopefully QuickTime X will regain its pro features in Lion.

As John says, the numbers you see in Format show you first ACTUAL resolution of your file and second DISPLAY APERTURE. It doesn't matter what the display aperture is for most applications since the actual resolution is what counts. You can reset the aperture settings here in Quicktime Player's Movie Properties window:
Change the setting to "Encoded Pixels" and you'll see the full 1920x1080. It is just some metadata for Quicktime Player's display, it will not change the actual resolution of your file.